Question

Из одного города в другой Одновременно навстречу друг другу вышли два поезда и встретились через 9 часов. Скорость одного поезда 48 км ч а скорость другого на 5 километров больше другого. Найдите расстояние между городами. С условием и двумя видами решения

Answer 1

48+5=53
53*9=477
48*9=432
477+432=909

Answer 2

1) 48+5= 53(км/ч)- скорость другого
2) 53+48= 101(км/ч) - скорость сближение или сумма двух скоростей
3)101*9=909(км)
Ответ: Расстояние 909 км.

Answer 3

Problem Analysis

We are given that two trains start simultaneously from two different cities and meet each other after 9 hours. The speed of one train is 48 km/h, and the speed of the other train is 5 km/h faster than the first train. We need to find the distance between the two cities.

Solution 1: Using Relative Speed

Let's assume the speed of the first train is x km/h. Then the speed of the second train is (x + 5) km/h.

To find the distance between the two cities, we can use the formula: Distance = Speed × Time

The time taken for both trains to meet is given as 9 hours. Since they are traveling towards each other, their relative speed is the sum of their individual speeds.

Using the formula, we can write the equation: Distance = (x + x + 5) × 9

Simplifying the equation: Distance = 2x + 5 × 9

Now we can substitute the value of x as 48 km/h (the speed of the first train) and solve for the distance.

Solution 2: Using Average Speed

Another approach is to use the concept of average speed. The average speed of the two trains combined is the total distance traveled divided by the total time taken.

Let's assume the distance between the two cities is d km.

The time taken by the first train to cover the distance is d/48 hours, and the time taken by the second train is d/(x + 5) hours.

The total time taken is given as 9 hours, so we can write the equation: d/48 + d/(x + 5) = 9

Now we can solve this equation to find the value of x and then substitute it back to find the distance.

Calculation

Let's calculate the distance using both solutions.

Solution 1: Using Relative Speed

Substituting the value of x as 48 km/h: Distance = (48 + 48 + 5) × 9 Distance = 101 × 9 Distance = 909 km

Solution 2: Using Average Speed

Solving the equation d/48 + d/(x + 5) = 9 for x: d/48 + d/(48 + 5) = 9 d/48 + d/53 = 9 (53d + 48d)/(48 × 53) = 9 101d = 9 × 48 × 53 d = (9 × 48 × 53)/101 d ≈ 909 km

Answer

The distance between the two cities is approximately 909 km.

Note: The calculations are approximate due to rounding off.